Such a system may be approximated on an air table or ice surface. The spring-mass system illustrates some common features of oscillation, namely the existence of an equilibrium and the damped and forced oscillations pdf of a restoring force which grows stronger the further the system deviates from equilibrium.
Thus, oscillations tend to decay with time unless there is some net source of energy into the system. The simplest description of this decay process can be illustrated by oscillation decay of the harmonic oscillator. Some systems can be excited by energy transfer from the environment. Two pendulums with the same period fixed on a string act as pair of coupled oscillators. The oscillation alternates between the two. In such cases, the behavior of each variable influences that of the others. More special cases are the coupled oscillators where energy alternates between two forms of oscillation.
The mathematics of oscillation deals with the quantification of the amount that a sequence or function tends to move between extremes. This page was last edited on 10 December 2017, at 21:01. Careful designs usually minimize unwanted vibrations. The studies of sound and vibration are closely related.
Hence, attempts to reduce noise are often related to issues of vibration. Examples of this type of vibration are pulling a child back on a swing and letting it go, or hitting a tuning fork and letting it ring. The disturbance can be a periodic and steady-state input, a transient input, or a random input. The periodic input can be a harmonic or a non-harmonic disturbance.
Examples of these types of vibration include a washing machine shaking due to an imbalance, transportation vibration caused by an engine or uneven road, or the vibration of a building during an earthquake. For linear systems, the frequency of the steady-state vibration response resulting from the application of a periodic, harmonic input is equal to the frequency of the applied force or motion, with the response magnitude being dependent on the actual mechanical system. When the energy of a vibrating system is gradually dissipated by friction and other resistances, the vibrations are said to be damped. The vibrations gradually reduce or change in frequency or intensity or cease and the system rests in its equilibrium position. Vibration testing is accomplished by introducing a forcing function into a structure, usually with some type of shaker. For higher frequencies, electrodynamic shakers are used. Generally, one or more “input” or “control” points located on the DUT-side of a fixture is kept at a specified acceleration.